Assignment 2: just for further interest

Because I was so intrigued about my insanely low temperature, I decided to use SPSS and calculate my stats without my two low extremes of 92.3 and 93.7.  In doing so, my stats changed quite significantly.

Mean = 97.05

Median = 97.15

Mode = 96.7

SD = 1.18

Variance = 1.385

Using these stats and comparing it to the actual population’s average I still got a standard deviation of -1.2 between my mean and the average of 98.25.  This -1.2 is still significantly more than .73.  I guess I really am just cold-blooded!!

Assignment 2: Five Points

1. a) I believe that the central tendency the most influence by extreme temperature values would be the median, but i also believe that it would significantly affect the mean as well. If there was a really high or a really value, that would make a greater range between the highest and lowest number, which would cause the median to be shifted, one way or the other depending on the outlier. I didn’t have much of an outlier; The point that seemed farthest away from the rest of the points was the 95.3. Without that point, the median of my data became 98.3, rather than 98.25. Although this is not a significant change, that specific point was not that far from my data. If it had been farther, i believe that the median would have changed more. The mean I think would also be affect. With the 95.3 in my data the mean was 98.3, although without that data point, the mean changes to 98.1. I believe that for this set of data that change is significant. If the outlier had been farther away from the rest of the data, I believe that the mean as well as the median would have changed more than it was.

     I believe that these extreme data values aren’t unusual. This could be attributed to randomness. Although I didn’t an extreme outlier in my data, my partner did.  The extreme points in the data values could be due to any number of events that could have affected any of the points in the data. I think that the extreme data points are just as reliable as the rest of the data points. Although they are extreme, I think that the randomness allows for extreme data values.

   b) While most people believe that the average body temperature is 98.6 degrees F, that is actually incorrect.  The correct average body temperature is 98.25 degrees F. This was found by Allen L. Shoemaker. The 98.6 degrees F is actually about 100 year outdated. This is due to the diurnal fluctuations and unreliable thermometers.

   c) My mean in my data was 98.3 degrees F. This is less than a tenth of a degree different from the average of all body temperatures. 98.3 – 98.25 = .05 degrees F. My body temperature is very close to the average body temperature. I don’t think that my body temperature is particularly unusual because it is so close to the mean.

   d) My body temperature is only .05 degrees F higher than the average body temperature. Since I am slightly above the average, and most women’s temperatures are slightly above men’s, I believe that I am a good representation of the female population. I believe that if I continued to take data, that my mean would fluctuate slightly but stay in the same general area. Taking more data would also increase the accuracy of my mean.

   e) To find your body temperature average in Celsius, Shoemaker wrote the formula to be C = (degrees F – 32) * 5/9). Therefore my temperature would be C = (98.3 -32) * 5/9. My mean temperature in degrees C is 36.83.

2. This assignment relates to our class discussions because it makes us use the different central tendencies to analyze our data.  It also adds on the randomess from the last assignment because it requires us to analyze out outliers and why they would be there.

3. I posted my caluculations under: Assignment 2: Calculations

4. Shoemaker, Allen L. What’s Normal? Temperature, Gender, and Heart Rate. Journal of Statistics Education. 4, 2(1996)

Mac Ewen, B. (2008, spring semester). Psychology 261.  Class lectures.  University of Mary Washington

5. I don’t believe that there were many weaknesses in the data because of the careful calculations, although there could always be human error in that. The most prominent weakness would be the with the SPSS program. In order to use the program, you must be in the lab and there are only certain times that I am able to get there.

Assignment 2: Calculations

These are the calculations that I found by hand/calculator:

Mean – 98.03

Median – 98.25

Mode – 98.1

SD with n – .92615

SD with n-1 – .94315

These are the calculations that i found using SPSS:

Mean -98.0286

Median – 98.2500

Mode – 98.10

SD – .94315

Varience – .890

Assignment 2: Five points

1.

a.  I think that standard deviation and mean are most influenced by extreme temperatures because those extreme temperatures are the ones that are really far from any other temperatures.  In calculating standard deviation, a person takes each value (or temperature) and subtracts the mean (which is calculated by adding all the values up and dividing by the total number of values).  In my temperatures, I had a temperature that was 92.3.  I believe that temperature probably lowered my mean.  My mean, 96.7-92.3 = 4.4.  That’s a pretty big difference for standard deviation.  When adding up all the differences, that particular value of 4.4 probably had some type of effect because it was so different from the others hence…it was an extreme.  I do not think that extreme values are rare or unusual.  I think they probably always occur, but I do not think we can relie on them.  Professor Mac Ewen was talking in class the other day about the 95% interval.  He said that there is an interval which cuts off the end 2.5% from both extremes and that interval is where a person can be most certain a point of data will occur.  In my case, obviously 92.3 is not going to be in that 95% interval.  I also remember taking a course with box-plots where we opted to cut out those extremes.  I feel that in cutting out the extremes, our data seemed more representative.  Although extreme cases probably always occur, they are extremes.   Just because something isn’t rare, doesn’t mean it’s common.  If one would look at extreme cases over the long run in comparison to 95% interval values, they might even state that extreme cases are rare, in comparison.  I personally think that randomness allows for things to be extreme.

b. According to Shoemaker’s article, 98.6 is not the average body temperature.  98.25 degrees F is the actual mean, and Shoemaker explains that 98.6 is 100 years old and probably miscalculated through bad thermometers, problems with Wunderlich’s original methodology, and diurnal fluctuations (Shoemaker 1996).  The article identified .73 as the standard deviation. 

c.  96.79 (my mean) – 98.25 (real population mean) = -1.46.  My body temperature is 2 standard deviations away from the real population’s mean.  I think that is pretty significant and unusual.  It seems like my body temperature would be on the extreme side and I would fall on the lower end of the bell curve.  This kind of makes sense to me because I am always cold.   Friends of mine always question what it wrong with me because I am always cold, and now I feel like I can say, “Hey, my body temperature is two standard deviations away from yours, so knock it off.” 

d.  Considering that my body temperature is so low, I do not feel like I am representative of the female population at all.  In fact, I feel like my temperature is probably lower than most boys’ temperatures.  I have already identified that my mean was probably affected by some of my extreme temperatures such as 92.3 and 93.7.  Perhaps if I took my temperature more often (such as the entire semester), those extremes wouldn’t have counted for that much.  At the same time, the fact that I had two rather low temperatures in five days, makes me wonder how many more low temperatures I would have throughout the entire semester.  So, personally, I’m not really sure I would ever be representative of the girls.  I think I’m just cold-blooded and deserve to be surrounded by snakes and reptiles in the Florida Keys. 

e.  To convert F into C, Yahoo answers has voted Dana 1981, Masters of Science’s way.  She says to subtract 32 and multiply by 5/9.  For my mean 96.79-32 = 64.79 * 5/9 = 35.99 degrees C.

2.  This assignment relates to our class discussions because it requires us to use different measures of central tendency as well as two forms of varience.  It also continues exploring randomness because it is a way we are putting our data in order despite its randomness.

3.  My data is posted under the title “Assignment 2: calculations.” 

4.  References

How do you turn °F into °C?.  26 January 2008.  <http://answers.yahoo.com/question/index?qid=20071229110526AAHVeKV>.

Mac Ewen, B. (2008, spring semester). Psychology 261.  Class lectures.  University of Mary Washington.Shoemaker, A. L. (1996). What’s normal?  Temperature, gender, and heart rate. Journal of Statistics Education. 4, (2).5.  I felt like this assignment was in general, pretty neat.  I enjoyed looking up celcius and reading the article.  I also liked realizing how cold I am.  The only flaw I found was limited access to SPSS.  I am a commuter student, and although I have been informed that I can rent SPSS…I think that is really pointless.  So, for the most part, I am done with my assignment, but because I do not have SPSS at home, I have to wait until 5pm tomorrow to figure out the SPSS stuff not to mention hope the lab isn’t randomly closed.  Also, I had trouble formatting my references…which is why they look funny and is randomly in a different font.

Assignment 2: my calculations

Calculator calculations

mean = 96.79

SD = 1.52 

σx = 1.50

Median = 97.05

Variance = 2.3104

Mode = 96.7

SPSS Calculations

Mean = 96.79

SD = 1.52

Median = 97.05

Mode = 96.7

Variance = 2.317

I have observed that all of my statistics were exactly the same between my calculator and SPSS, except the variance. 

Assignment 1: Final 5 Points

1.  This week had to do with randomness.  Randomness is hard to define without using the word ‘random’ in it, but is pretty much a light version of chaos or without order.  A great example of randomness is flipping a coin; landing on heads or tails occurs at random.  

          A random event is an event that occurs in no particular order.  This is different from a systematic event which occurs on the basis of a certain slant or bias.  An example of a random event would be a squirrel running across a lawn.  No one can really say that there is order to the squirrel running across a lawn, nor could they predict it to occur.  (Perhaps if you really dissect this example you could find how a squirrel running across a lawn is NOT random, but please just look at it at the surface.)  An example of a systematic event would be if we were conducting an experiment on eye sight, and for some reason, all the people we interviewed wore glasses/contacts of which was unbeknown to us.  The people wearing corrective lenses would skew our results systematically.

      We do not think it is possible to predict our temperature.  We can make an estimation such as, “I think it will be lower (or at) approximately 98.6 degrees,” but we could never predict it to a T (ie: Erin’s temperature will be exactly 98.4).  We really don’t think that anything is solid-fool-proof predictable.  This being said, we both feel that as one gets closer to an event occurring, the easier it is to predict.  For instances, we cannot predict the weather–at all, but on a day when it feels like rain, especially in the summer, we both feel that we can usually predict that it will rain.  We find that we are also very good at predicting movies, and people’s reactions/sayings.  We’re not always 100% right all the time, nor are we super specific.  There are simply too many things in this world that can get it the way and change an outcome.  It’s like the butterfly effect.

     Erin uses a heating blanket at night which could be viewed as her systematic event.  It skewed her body temperature in the mornings.  I found that whenever I remembered to take my temperature it was usually right after I had walked inside from outside (which could maybe account for why my temperatures were so low!).  The cold weather probably systematically affected both of our temperatures.

     We were not sure if our seven sources needed to be life related or temperature related.  We came up with seven temperature related sources of random variation: 1) the environmental temperature, 2) working out, 3) emotional state, 4) time of day, 5) taking a shower, 6) heating blanket, and 7) drinking cold or hot beverages.

2.  This week’s weekly project relates to class lecture because body temperature is pretty random.  It fluctuates for too many reasons to determine its actual cause and outcome.

3.  Graph was posted in previous post.

4.  Our sources included our digital thermometers and class notes/power points.

Mac Ewen, B. (2008, spring semester). Psychology 261.  Class lectures.  University of  

          Mary Washington.

5.  Erin and I both feel that a weakness in the data collection was that it has been so cold lately.  We keep going in and out of heat and cold, and both of us feel that that affected our change in temperature the most.  Although we were not able to predict our temperature, we were able to estimate if it would be significantly below 98.6 if we had just come from outside.  For some reason, we noticed that my temperature was significantly lower than Erin’s.  Erin’s temperature didn’t seem to go below 97 degrees, while mine went much lower, perhaps it may have been simply a malfunction of my thermometer. 

Assignment 1: Final graph

Assignment 1: rough version of 5 points

1.  This week had to do with randomness.  Randomness is hard to define without using the word ‘random’ in it, but is pretty much a light version of chaos or without order.  A great example of randomness is flipping a coin; landing on heads or tails occurs at random.  

          A random event is an event that occurs in no particular order.  This is different from a systematic event which occurs cyclically.  An example of a random event would be a squirrel running across a lawn.  No one can really say that there is order to the squirrel running across a lawn, nor could they predict it to occur.  (Perhaps if you really dissect this example you could find how a squirrel running across a lawn is NOT random, but please just look at it at the surface.)  An example of a systematic event would be the sun rising and setting.  It is an event that occurs everyday, can be timed, predicted, and is cyclical.

      I do not think it is possible to predict my temperature.  I can make an estimation such as, “I think it will be lower (or at) approximately 98.6 degrees,” but I could never predict it to a T.  I really don’t think that anything is solid-fool-proof predictable.  This being said, I feel that as one gets closer to an event occurring, the easier it is to predict.  For instances, I cannot predict the weather–at all, but on a day when it feels like rain, especially in the summer, I can usually predict that it will rain.  I am also very good at predicting movies, and people’s reactions/sayings.  I am not always 100% right all the time, nor am I specific.  There are simply too many things in this world that can get it the way and change an outcome.  It’s like the butterfly effect.

     I am not sure of systematic effects from my data yet because I am still collecting, but I have noticed the night and day difference.

     seven sources…for body temperature????

2.  This week’s weekly project relates to class lecture because body temperature is pretty random.  It fluctuates for no apparent, orderly reason.

3.  Graph would go here

4.  My sources included my digital thermometer and class notes.

5.  Erin and I both feel that a weakness in the data collection was that it has been so cold lately.  We keep going in and out of heat and cold, and both of us feel that that affected our change in temperature the most.  Although we were not able to predict our temperature, we were able to estimate if it would be significantly below 98.6 if we had just come from outside. 

Assignment 1: Seven Sources of Random Variation

Here are some things that I found affected my body temperature this week.

1.  the enviornment’s temperature (if in a heated room or by a fire, or in the cold snow)

2.  if I worked-out and broke a sweat

3.  if I was nervous/embarassed

4.  what time of day it was

5.  if I had just gotten out of the shower

Erin,

Can you come up with any others?  Also, question:  the assignment says “identify at least 7 other sources of random variation that affect your life”  Does this mean temperature-wise?  Or just in general?

Assignment 1: Rough Summary #1

1) To show the randomness in everyday life, we toook our temperature for every 2 hour period for 12 hours. We did this for 5 days. This resulted in 35 data points for our graph.

2) This assignment related to the statistical topic of randomness. By doing this experiment we have been able to see the results on the graph of the different temperatures of our body. This temperature is random because any number of different factors could cause it to change and we can not predict the outcome.

4) Notes from class on randomness

5) One of the weaknesses of the statistics would be that it is winter so everyone’s body temperature would change when they went outside as compared to their temperatures inside. Alothough this could also be considered a strength because we are studying randomness, this could be seen as one of the many factors that would affect the unpredictable outcome. Another weakness is that the temperature isn’t taken with a set amount of time between them. For example, one temperature could be taken at 1:45 and then the next at 2:05 and then not again until 5:00.